[About swapping a defective Oyster for a new one]
I also wonder whether my auto top-up has made it across to the new card.

[and...]
Incidentally, the web site still thinks I have the old card, with
the old balance, and doesn't know about the new one. Maybe I should
attempt to register it?

Well, I did register the new card - although I would have thought it
should already have been associated with my account at the station.
The new card *doesn't* have auto top-up, and the old card is still
showing, with the balance it had when I handed it in.

This can't be the way it is supposed to work?!!

You have to email ask Oyster and ask for your old card to be "disassociated"
from your account.

Auto top up cannot be transferred by the station staff.